What is the evidence thr yhu glewxh5p5z6q9-a)5r/o s 3 l)qn( w4bfxat sound travels as a wave?

What is the evidence that sou f rbcj61kfj,ngf4: f1nd is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a sb 5;lr ,0fludwtring to the bottoms of two paper cups. When the string is stretched and a child speaks into onedllr b,u5wf;0 cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expecly* xce5r s*x6t the frequency or wavelength to change xlr e*x*56cys?

What evidence can you give 4 s;eqna373uz5pffoe4j bv,gthat the speed of sound in air does not depend significantly on frg3j4 ab,7 v4qfp so;zenf5eu3equency?

The voice of a person who has inha 0(ou a6g) b2s9pwr me4twc4jaled helium sounds very high-pitched. Why?

How will the air temperature in a r ji3lode6qv3 p-mw3f 1oom affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude *wo ubi;* -8k(d.hc4kc9ns d b ckpte,of sounds in various frequency ranges. (An example is a car muffki8-ckwps., tcnuhbck*;* edd 4o 9b(ler.)

Why are the frets on a guitar (Fig. 12–30)+wkl9t6cu*ku8(og1 k-tiri z2k3h s(f-gp u x spaced closer together as you move up the fingerboard toward the i6-k(kgp2c kk9it h +zx rf8g-w1tuos*u3 (ul bridge?

A noisy truck approaches you from behind a building. Initially you hear ()engc ;1 sti-ek*qbuit but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more g- (ee)n*1 ;qtbksicu of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas mmx1:h uhl0uv4:/vo2 z8 nazc beats can be said to be due to “interfereu0v1:cxm/4al hz m2nhvz 8o:unce in time.” Explain.

In Fig. 12–16, if the frequency of the spek5 /a j)vejir cs:6je(akers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or closer togethjjec k:rsj(56 /)aiev er?

Traditional methods of protecting the hearr, a, -p.lwseying of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then fs ,ypa,-wl er.eeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of as a sea f,1n( a8f5r8h ykcpuperposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In whic(fkfhe8apcn,r8a1y 5 h of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer mo0g 1tik2rien9q 25w5 kwbaf+wafzw ;1ve in the same direction, with the same velociw;wa 5 qtkf9in1f w12br i5+gaw 20zekty? Explain.

If a wind is blowing,39t j05z,uhf rf6x 2hka)mdrp will this alter the frequency of the sound heard by a person at rest with respect th2fk5au6 t3h0m9rjrx) pf ,zdo the source? Is the wavelength or velocity changed?

Figure 12–32 shows var2kz17 wa3aa jfious positions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistlaa w37jfk za12e? Explain your reasoning.

  A hiker determines the length of a lake by listening jcj1x6gj;f. fxug50 xr a11c kfor the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shoutigf a fj1c16uj.xj ;kgx1xc0 5rng. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He+ vp)* om s*mm-d8cx1cehd .lz hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is*d)-l. vpedmxm+c1*chm 8zso 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengs/o4i2 8avy 0yjq hxj5ths in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat bl7vbph /x 4+zis drifting just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfh4 l bpx/b7v+zire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The o*1dhh c6b7za splash it makes when striking the water beza1 7h6 cdb*ohlow is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, see;4oiwn tnvwl16hs1y vgc+6q4s a huge stone strike the concrete pavement. A moment later two4cvng6 6i w11vwosn4ql;t+hy sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of kx ilh;9e agrkx30:* pdistance by the “5-second ruleexrp;*akhlk :xi039 g” for estimating the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensitz+3jb uj-2oj gy of a sound at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a soundrd+sd *e04ykv whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneously at 5ueof98 fyzd6p l -s53o*t mova certain place, what will be the sound level if only one is exploded? [Hint: Add io vy ls95683*z mefoutop-d 5fntensities, not dB’s.]    dB

  A person standing a certain distance from an airpla,v19e s(pnlzu ne with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would thisz9pe( ,vnl1 su person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signalo-2s oql 1n*oesf4k4g-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? sn 4f2o 4olgko-se q1*58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sounpw2c6( exf tyw+v g/: dncw/)od from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniforxvec2w:dt (cny w6/fg) /wop+mly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an,)-(a6mt nhlu qi edf( eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modj8-+kvaqq3lyu-pb p mf8 v6h (est amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you wov p(p 36bf - amyjqvq+8kul-8huld expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m in front of a 0sv ,;tawto m; b;g/uhwgb;0;,m;to/ suha v tloudspeaker on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a diohv fq(u7g i- utx4x0)fference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sound gv oxx7tqu)(if0uh -4s whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) byl /d,;s(xy./ a7jel0rpsnvn l what factor will the intensity increas/r/7,j yd(sp .lvnex al 0sln;e? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twic/cro rqn0g ,lv9i8: :c h5mthfe the frequency0n,rg5:h89c vo q h:rmlct/fi of the other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a soug. +tifjd+y -pnd wave in air that corresponds to a displacement amplitude of vibrating air molegpd+tfi+- y.jcules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level t nsp (33xx/knbo seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig3k nb/xp(xs 3n. 12–6.)    dB

What are the lowest and highest f86a 0lhfrz gv)wa4**up 2vgh crequencies that an ear can detect when the sound level is 30 dB? (See f0ahlagr cv8h*)*z4w6u v2g pFig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What id fx qp7r8;p7os the ratio of highepo ;7 f7pxdr8qst to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. The length ofmix mqaft*5y z 5u9:z4,-bwvf the vibrating portion is 32 cm, and it has a mass of 0.35 g.5, 4* y9qb t5wxzuam:mfi-fv z Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and. l5f4f9 oknuwhlds d t0p.9c, first three audible overtones dclfo 5pf.tk49du,9 n0w lh.sif the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing across the top of xfjdn2j+) w,hy*wb .dan empty soda bottle that is 18 cm deep, if you assumed it wajbdn+h,)yfdxww *j2 .s a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning thexo 5 qchv-hui67*v 3vmry4 4qkfdm /p) range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes revmpq64yq* u57fh mcrv xhoikv/4 d-)3quired? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third har7tx mkmkmn7( 1monic. What will be its fundame 71m xnmt7k(mkntal frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.x+8uthr 8.oby 73 m long and is tuned to play E above middle C8x+ b.ro8uht y (330 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middl874dn (hpvf s)gaoac*e C (262 Hz) when the tempd *sfpnoa(ah8gcv47) erature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at 20hhm stji:f9 ;5qf.+gy $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpietg(j x.;fsb+x ce of the flute in Example 12–10 should the hole be that must be uncovered to play D above middle C at 294f+bsj gxx.;t( Hz?    m

  (a) At T = 20 $^{\circ} $C how long must an open organ pipe be to have a fundamental frequency of 294 Hz?    m
(b) If this pipe is filled with helium, what is its fundamental frequency?   Hz

  A particular organ pipe can reso cmbvzk8d eaw 4ms+l/-i()ng11dj/sy nate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a dcm sg we/i8/)4szvy1jk1ld+( -nabmclosed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It s*m2mu0,r brd qra;h;*gy1dkresonates at two successive harmonics of frequencies 275 Hz and 330 Hz. What rdrs, dr20uk*1*y; b qmhg; mais
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 n1yak* 5fbz etn/ 2l,m/tsx6e$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.14-m-long organ g a/o+8fg( k6t w5ogsip g8gat /+5oow(gsf 6ikipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is or d/wzzps(: mrn-7x0qc :rzf* pen to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answezrdq*-mxr(0zn:z7f /wc sp r :r to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one bea f6dwbj rs ,onz3y2,n3t every 2.0 s when trying to adjust two strings, one of which is sounding 440 2r6j,y dnwoz 33s nb,fHz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if42 tl*a3qk5oyreob :j middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (b2x yp(9 otxqe7rand X) operates at an unknown frequency. If neither whistle can be heard byx 2t9o qxype7( humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4o*5 .qpplsp4blw+u*h e2r6om h ev17d beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reab 7lop mres 2 4* d5wl*hp6ohq.ep+v1usoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension in one cq,yny nn8hq) 8i-ya (string is then decreased by 2.0%. What will be the beat frequency heard when the two strings,nhycy8 i a- n)8(nyqq are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will bmc:1yu( cbs 4te heard if two identical flutes each try to play middle C (262 Hz), ub:t (y4sc 1mcbut one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, i1f3ri;f;wlp 5) uqq sand C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What usrq; 5;fp w li13q)ifare the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 i4; d s-u0gcvi*it s9t3kzz9vm from one speaker and 3.5 tc z3i ug9iv0t 4;ss*ik-vd9z0 m from the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to 2fbai8 ue7d(( / tmlnbbe vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s wh/7(u8n b(d2 atimefblen they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound ob) a j:duue*vv s7ze;1f wavelengths 2.64 m and 2.76 m in air. How many beats per second willauv* j zveeb1:s d)u7; be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s0hxr. q5t;vhtkkv98n siren is 1550 Hz when at rest. Wth n0hr ;5t.kqvvxk98 hat frequency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. Wy38cgq 9q )c fuo29knihat frequency do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed o39 qcf ycnq uki)go298f 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in bjj*ojn1( 8amfrequency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/smo( 81jj*bn ja Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. When o sjyw xx,(+z1+ey-bx une is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a+ we1y,xxjs(xz-ub + y beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends ou/ h hv;pzd(bwel6il6 ;t ultrasonic sound waves at 50.0 kHz and receives them returned from an object moving dirhi6ve;/hlzp6 ;d wl( bectly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emits an ucfby7lg*vlp rlr -, 5bb;dnxri9 62l0 ltrasonic lgf b dbl0b ,pivr5r-xl7r2 ln;*69cysound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler exp5r0to calh 5qrsov 7db9/ ctavh /(+5ueriments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speedrtlh c/vdo br/ +asc (5o 9htqu0v5a57 of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow s23.q a9/hmd vrki5n/keid xo3dx3 -lkpeeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue ek/9rhv2-x d q / 5 nkd.ma3doixi3l3kis taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of fr3 jv.dk fz/p(aequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When tha) l.as- i*6z brf:vlme wind velocity is 12 m/s from the north, what frequency will observers hear who are located, at rest, *m)ibz6sv.a a r:-lfl
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if mf1c5r3bfwv 5its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the sv*6mi3:q3m (c-3qmlvqa y oyl+a 3ber peed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplaoq3mqcy3ivlmm6v+ar( bl33a y* q -e:ne’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planhxc+xz;8ng7lq;vm0aq+jk2 n r i*d h 3et where the speed of sound is only zdh ; qn mhv83g*2+a07r +qlnkxxcji;about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine the shock wave 7jd yc7 ;a4owqqol* k*angle it pla7 7*; 4oocqqw*y jdkroduces
(a) in the air just before entering the ocean, $\approx$    (Round to the nearest integer)
(b) in the water just after entering.    $^{\circ} $
Assume T = 20 $^{\circ} $C

Show that the angle ,m5yxvw.b: c x$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km above thie5ux s9vnu 0b,y)k ;re ground flyingxrnubk;, 5 sy) 9ive0u faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sj a a2.2b4ekknwpbs-4ound pulses downward from the bottom obknb4aaj2pw. -ke2 s4 f the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible range?d9 *zp.c,0dj iy. hpqb $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe *e2 y 8ee;nm59dgex7 ktlut)3kfa6ls symphony. It consists of many plastic pipes of various lengths, which are open on both ends. xgn d 2ym8l7af5et9*ue ks)lte ;k 3e6
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a lrmlq8ut *wl/6h 358 68uxon xeq;hya sound close to the threshold of human hearing (0 dB). What wiltmwl eu 5ahqx*l; un6 h68 /8qx3r8ylol be the sound level of 1000 such mosquitoes?    dB

  What is the resultant su73yq cpe5g6udz uoas0p7 o20ound level when an 82-dB sound and an 87-dB sound are hearo u3 y0az7dcuuqsgo620pe57pd simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in thkw3zr bv yy;rl3mj6 rk;a*2+ie open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiate;izm3 byrvk 6rr32+wa;*y kljs equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The powu 6ag)-q xybh1ikhd:7er output drops by 10 dB at 15 kHz. What is the power output y: 6guk17d-bh hai)qxin watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective dev zln,l1 d/pr m9f 18k2i0eiukjices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear ail1zk j98 ,1 0l/ ueikpfmr2ndt a distance of 30 m from a jet airplane engine?    W

  In audio and communications syst.b3-sv*oulb+ h2mkw7mzlod * ems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is t777mbrg/yx ht(o5 rsi b6yzj5uned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm ff+ul 4t78; vmzi9.9rmzpm,,z kfte nlong between fixed points with a fundamental frequency of 440 Hz and a m9 tr,;e,f8 9pm4zv+kziulf7.z mm ft nass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration au0v*t9hqjz4 xcf 5 (ptyh:2lobove a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distajf2p:hxc5yq40ov hut ( zl*t 9nce from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is0d7vel50s;*dezkl u2j* qtpe b.h 3ax open at one end and also 75 cm long. How much tension should uq7 edllx 5epvz.t*d0a3eh 2kb;0*jsbe in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to re+zc: +ghu)trvsonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz ran+o zww;fk+b+v 2/vxjs1xa t k(ge coming from two sources. The sound is loudes x+jvbokk/v+zw 1+ twas(f; x2t at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary:yap. 6*8 kiw3h+u.fx la l d5z.dwcat. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What lx5wyk+:dpdc a8w6 * . .lt3z. ihuafais the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches yli-z*c9 aw7k ib8ue7i ou is 538 Hz. After it passes you, its frequency is meas -lc7 b9zii7u8e *akiwured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars jurd383/0ap ubbh)bhp 4vb5 xaz -mwn /yst by listening to the difference in pitch of the engine noise between approau5-b/0 ad 3vzb3b4hnpr8)a whpy x/mbching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beatduq0h*0x go:cv 3ou)i frequency of 11 Hz. The shorter one is 2.40 m x0oduohv)i 3*uqc0g:long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad cat (*ar8jbr v8w 3q6tvjr as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the p6ar 8w qr(3bvt8tjj *vosition A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 mkm9( 4c9icf xn(yf)j9.pwx yjp0o yb. /s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from thi(x. cp0pwfyoyf )x9j jy mk499n.( bce red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at)c 0/3fli l2isfl s 6ky66mlxyix49xt speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency ot sl6k9xc3xi )fyy/i06mll4i2sf6 lxf the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high freq xhdh6sg-i4t**l : ohuuency sound pulses as it approaches a moth. The pulses are aohd4xh *ihu*t :s-6g lpproximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) wa gnnyk7 se,.jm3 -lfht-ru*e 8s once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it i*g -u-rhs en3t 7yen mfj,k8l.s called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised q+ojbu h uz8a+q-*ag4a 6a2sdby the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standin4+a+g dubq 6o8-jsaaqza *h2ug waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involv4w h0p.wjxiy7es a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. 4yi0 xw w.p7hjFor a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the hk2k/af2/b /liwms ztu (n9uw5 uman ear at a frequency of about 1000 Hz is 9zlu/kf w/ u mk5stw(/ia2n b2$I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hears fi fz+7et;h 1gn/pbpz4f 45ob the sonic boom 1.5 min after the plane passes directne71f/ 54f;zothpi gp +b4b fzly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbocy7r nkb7vd ez(o* 4-wat is 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h